Noise-driven switching between limit cycles and adaptability in a small-dimensional excitable network with balanced coupling

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 3, 2006, Pages

  Safonov, Leonid A ^a   Yamamoto, Yoshiharu ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FITZHUGH-NAGUMO EQUATIONS; FREQUENCY OSCILLATIONS; OSCILLATORY STATES;

ADAPTIVE CONTROL SYSTEMS; ELECTRIC EXCITATION; OSCILLATIONS; SPURIOUS SIGNAL NOISE;

SWITCHING CIRCUITS;

ACTION POTENTIAL; ADAPTATION; ANIMAL; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; EXCITATORY POSTSYNAPTIC POTENTIAL; FEEDBACK SYSTEM; HUMAN; NERVE CELL; NERVE CELL NETWORK; NERVE CELL PLASTICITY; PHYSIOLOGY; STATISTICAL MODEL; STATISTICS; SYNAPTIC TRANSMISSION;

ACTION POTENTIALS; ADAPTATION, PHYSIOLOGICAL; ANIMALS; BIOLOGICAL CLOCKS; EXCITATORY POSTSYNAPTIC POTENTIALS; FEEDBACK; HUMANS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NERVE NET; NEURONAL PLASTICITY; NEURONS; STOCHASTIC PROCESSES; SYNAPTIC TRANSMISSION;

EID: 33645033648     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.031914     Document Type: Article

References (61)

1. A. T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980).
2. L. Glass, Nature (London) NATUAS 0028-0836 10.1038/35065745 410, 277 (2001).
3. R. FitzHugh, Biophys. J. BIOJAU 0006-3495 1, 445 (1961);
4. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE PIREAE 0096-8390 50, 2061 (1960).
5. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) JPHYA7 0022-3751 117, 500 (1952).
6. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
7. K. Ikeda, K. Matsumoto, and K. Otsuka, Prog. Theor. Phys. Suppl. PTPSEP 0375-9687 99, 295 (1989);
8. K. Kaneko, Physica D PDNPDT 0167-2789 10.1016/0167-2789(90)90119-A 41, 137 (1990);
9. K. Kaneko and I. Tsuda, Chaos CHAOEH 1054-1500 10.1063/1.1607783 13, 926 (2003).
10. A. Takamatsu, R. Tanaka, and T. Fujii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.228102 92, 228102 (2004);
11. A. Takamatsu, R. Tanaka, H. Yamada, T. Nakagaki, T. Fujii, and I. Endo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.078102 87, 078102 (2001);
12. A. Takamatsu, T. Fujii, and I. Endo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2026 85, 2026 (2000).
13. K. Wiesenfeld and F. Moss, Nature (London) NATUAS 0028-0836 10.1038/373033a0 373, 33 (1995).
14. B. Lindner and L. Schimansky-Geier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.7270 60, 7270 (1999);
15. S. G. Lee, A. Neiman, and S. Kim, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.3292 57, 3292 (1998).
16. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
17. R. L. Honeycutt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.600 45, 600 (1992).
18. The Floquet multipliers are calculated using XPPAUT 5.85 (http://www.math.pitt.edu/~bard/xpp/xpp.html).
19. S. A. Campbell and M. Waite, Nonlinear Anal. Theory, Methods Appl. NOANDD 0362-546X 47, 1093 (2001).
20. P.-L. Gong and J.-X. Xu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.031906 63, 031906 (2001).
21. M. Rabinovich, R. Huerta, M. Bazhenov, A. K. Kozlov, and H. D. I. Abarbanel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.6418 58, 6418 (1998).
22. W. J. Freeman, Chaos CHAOEH 1054-1500 10.1063/1.1596553 13, 1067 (2003).
23. L. M. Kay, Chaos CHAOEH 1054-1500 10.1063/1.1596071 13, 1057 (2003).
24. A. Raffone and C. van Leeuven, Chaos CHAOEH 1054-1500 13, 933 (2003).
25. S. K. Han and D. E. Postnov, Chaos CHAOEH 1054-1500 10.1063/1.1598691 13, 1105 (2003).
26. S. Nara, Chaos CHAOEH 1054-1500 10.1063/1.1604251 13, 1110 (2003).
27. H. Kitajima, T. Yoshinaga, K. Aihara, and H. Kawakami, Chaos CHAOEH 1054-1500 10.1063/1.1601912 13, 1122 (2003).
28. H. Fujii and I. Tsuda, Neurocomputing NRCGEO 0925-2312 58-60, 151 (2004).
29. V. S. Afraimovich, V. P. Zhigulin, and M. I. Rabinovich, Chaos CHAOEH 1054-1500 10.1063/1.1819625 14, 1123 (2004);
30. A. Venaille, P. Varona, and M. I. Rabinovich, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.061909 71, 061909 (2005).
31. F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.1217 49, 1217 (1982);
32. F. T. Arecchi, Chaos CHAOEH 1054-1500 10.1063/1.165847 1, 357 (1991).
33. S. Kraut, U. Feudel, and C. Grebogi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.5253 59, 5253 (1999).
34. C. Masoller, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00506-7 168, 171 (2002).
35. N. G. Stocks, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.041114 63, 041114 (2001);
36. D. Rousseau, F. Duan, and F. Chapeau-Blondeau, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.031107 68, 031107 (2003).
37. C. van Vreeswijk and H. Sompolinsky, Science SCIEAS 0036-8075 10.1126/science.274.5293.1724 274, 1724 (1996);
38. C. van Vreeswijk and H. Sompolinsky, Neural Comput. NEUCEB 0899-7667 10.1162/089976698300017214 10, 1321 (1998).
39. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.041903 67, 041903 (2003).
40. F. Varela, J.-P. Lachaux, E. Rodriguez, and J. Martinerie, Nat. Rev. Neurosci. NRNAAN 1471-003X 10.1038/35067550 2, 229 (2001).
41. J. K. Douglas, L. Wilkens, E. Pantazelou, and F. Moss, Nature (London) NATUAS 0028-0836 10.1038/365337a0 365, 337 (1993);
42. J. E. Levin and J. P. Miller, Nature (London) NATUAS 0028-0836 10.1038/380165a0 380, 165 (1996);
43. J. J. Collins, T. T. Imhoff, and P. Grigg, J. Neurophysiol. JONEA4 0022-3077 76, 642 (1996);
44. D. Nozaki, D. J. Mar, P. Grigg, and J. J. Collins, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2402 82, 2402 (1999).
45. D. F. Russell, L. A. Wilkens, and F. Moss, Nature (London) NATUAS 0028-0836 10.1038/46279 402, 291 (1999).
46. J. J. Collins, T. T. Imhoff, and P. Grigg, Nature (London) NATUAS 0028-0836 10.1038/383770a0 383, 770 (1996);
47. K. A. Richardson, T. T. Imhoff, P. Grigg, and J. J. Collins, Chaos CHAOEH 1054-1500 10.1063/1.166341 8, 599 (1998);
48. E. Simonotto, M. Riani, C. Seife, M. Roberts, J. Twitty, and F. Moss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.1186 78, 1186 (1997).
49. I. Hidaka, D. Nozaki, and Y. Yamamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3740 85, 3740 (2000).
50. T. Mori and S. Kai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.218101 88, 218101 (2002).
51. K. Kitajo, D. Nozaki, L. M. Ward, and Y. Yamamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.218103 90, 218103 (2003).
52. R. Soma, D. Nozaki, S. Kwak, and Y. Yamamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.078101 91, 078101 (2003).
53. S. M. Barman and G. L. Gebber, J. Neurophysiol. JONEA4 0022-3077 57, 1410 (1987);
54. S. M. Barman and G. L. Gebber, J. Neurophysiol. JONEA4 0022-3077 61, 1011 (1989);
55. S. M. Barman, H. S. Orer, and G. L. Gebber, J. Neurophysiol. JONEA4 0022-3077 74, 2295 (1995).
56. M. Yamamoto, Brain Res. BRREAP 0006-8993 10.1016/0006-8993(86)91305-3 366, 279 (1986);
57. M. C. Teich, IEEE Trans. Biomed. Eng. IEBEAX 0018-9294 10.1109/10.16460 BME-36, 150 (1989);
58. C. D. Lewis, J. Neurophysiol. JONEA4 0022-3077 85, 1614 (2001).
59. P. A. Tass, T. Fieseler, J. Dammers, K. Dolan, P. Morosan, M. Majtanik, F. Boers, A. Muren, K. Zilles, and G. R. Fink, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.088101 90, 088101 (2003).
60. J. M. Hurtado, L. L. Rubchinsky, and K. A. Sigvart, J. Neurophysiol. JONEA4 0022-3077 10.1152/jn.00853.2003 91, 1883 (2003);
61. A. A. Kuhn, D. Williams, A. Kupsch, P. Limusin, M. Hariz, G. H. Schneider, K. Yarrow, and P. Brown, Brain BRAIAK 0006-8950 127, 735 (2004).